Question: There are 10 people in a room. If everyone shakes everyone else's hand exactly once, how many handshakes occur?
Solution: Given 10 people, each person shakes the hands of 9 other people. The following is almost the answer. $10 \times 9 = 90$ We have double counted the handshakes though, since Luis shaking Gabriela's hand is the same handshake as Gabriela shaking Luis's hand. Therefore, the following is the correct answer. $\dfrac{10 \times 9}{2} = 45$